The invention concerns the reconstruction of a three-dimensional image of an object from a set of two-dimensional projected images of the object obtained for different positions of a camera around the object.
Its application is of particular interest in the medical field, in which reconstruction of the internal structures of a patient being examined is undertaken, and especially the reconstruction of angiographic images, that is, to obtain images of vascular trees opacified by injection of a contrast product.
The invention can, however, find applications in other fields, notably, in nondestructive industrial control, in which examinations of the same type as medical examinations are performed.
In the medical field two-dimensional projected images of the object, a patient's head, for example, are generally obtained by rotation of an X-ray camera turning around the object
There are essentially two types of reconstruction algorithms in X-ray imaging.
A first type provides for a calculation of back projection and filtering or even a reconstruction by Fourier transform in several dimensions.
A second type, involved in the present invention, concerns iterative methods of reconstruction also called algebraic. The principle of such an algebraic algorithm is well known to the expert and has already been the subject of numerous published papers. One can notably cite Gordon, Bender and Herman, "Algebraic Reconstruction Technic for Three-Dimensional Electron Microscopy and X-ray Photography," Journal THEO. BIOL. 29, pages 471 to 781 (1970); Anil K. Jain, "Fundamentals of Digital Image Processing," Prentice Hall Information and System Sciences Series, Thomas Kailath Series Edition, or French patent Applications Nos. 89 03606 or 89 16906.
After a calibration of the camera used to determine, notably, the parameters of projection in the projection planes of the acquired images, of an observed volume broken down into elementary volume elements or voxels (those calibration parameters forming projection matrices), the algebraic image reconstruction algorithm is used to reconstruct the three-dimensional volume from those two-dimensional projected images. The basic principle of the algorithm is to initialize the voxels of the volume to a predetermined initial value, a zero value, for example, and to repeat a number of times the following operations: projection of voxels in the plane of each acquired image so as to obtain a virtual image, determination of the difference between the projected volume (virtual image) and the corresponding acquired image and then back projection of the difference in volume. After a number of iterations, an estimated value representative of the density of the contrast product injected in the vessels X-rayed is obtained for each voxel, which makes it possible to visualize in three dimensions the cartography of those X-rayed vessels.
Such an algorithm necessitates determining a great number of times, typically several million times, the projection of a voxel, using the different projection matrices.
If the algorithm is not optimized, determination of the projection of a voxel requires at least nine additions, ten multiplications and one division, which is a severe drain on the calculation time of the microprocessor incorporating the algorithm and, consequently, on the duration of image reconstruction.